Experimental Campaign
Geometry, Materials, and Monitoring Setup
A prismatic concrete specimen (0.60 × 0.30 × 0.60 m³) was designed to generate measurable thermal gradients while remaining suitable for numerical modelling. The lateral faces and base were insulated using polystyrene and plywood to limit heat dissipation and promote internal temperature development, as shown in Figure 1.
The concrete mix included 400 kg/m³ of cement (Type I 42.5R), with calcareous aggregates and mixed sands. Casting was performed in a controlled chamber at 20°C and 50% relative humidity.
Temperature was monitored using thermocouples (Type K) and PT100 sensors. Strain measurements were obtained using two embedded vibrating wire strain gauges:
- VWM (metallic casing), higher stiffness and lower temperature sensitivity
- VWP (plastic casing), lower stiffness and higher temperature sensitivity
Sensors were placed symmetrically and at two levels along the specimen height to capture vertical gradients, as shown in Figure 2.
Problem Definition: Measuring Strain at Early Ages
Strain measurement at early ages is inherently uncertain. Before sufficient stiffness develops, sensors are not fully bonded to the concrete. This introduces two key challenges:
- Determining the instant of solidarization, when the sensor begins to follow concrete deformation
- Accounting for temperature sensitivity in the sensor response prior to full bonding
These effects distort strain readings during the initial hours, when thermal expansion is most significant. As a result, early-age strain data must be interpreted as a bounded response rather than a direct measurement, consistent with the discussion in the source study.
Experimental Results
Temperature Development
Temperature development followed typical hydration behavior, shown in Figure 3:
- Rapid heating immediately after casting
- Peak temperatures of approximately 64°C at the bottom and 55°C at the top
- Cooling phase beginning at approximately 20 hours
- Thermal equilibrium reached at approximately 160 hours
Figure 3. Temperature development measured by strain gauge sensors
Temperature distributions along the boundaries – shown in Figure 4 – confirm the influence of insulation, with higher temperature concentrations at the base.
Total Strain Behaviour
Measured total strains (Figure 5) show a clear vertical gradient consistent with the temperature field.
Significant differences between VWM and VWP sensors during the heating phase are attributed to:
- Earlier solidarization of the plastic sensor
- Higher temperature sensitivity prior to bonding
During the cooling phase, both sensors showed consistent behavior, confirming adequate mechanical coupling with hardened concrete.
The study demonstrates that early-age strain should be interpreted within bounds, as shown in Figure 6:
- Raw metallic sensor output represents an upper bound
- Corrected signal, excluding pre-solidarization effects, represents a lower bound
Thermo-Mechanical Modeling in DIANA
Model Framework
The numerical approach follows a sequential thermo-mechanical formulation:
Thermal Analysis
The temperature field is governed by transient heat conduction with internal heat generation:
- Hydration kinetics based on Arrhenius-type formulation
- Heat transfer through convection
- Explicit modeling of concrete, insulation, and formwork materials
Mechanical Framework
The mechanical response incorporates hydration-driven material development:
- Equivalent age formulation for maturity
- Elastic modulus development based on Eurocode 2
- Viscoelastic creep modeled using the Double Power Law
- Autogenous shrinkage measured experimentally
Model Setup
The concrete prism was discretized using a three-dimensional finite element mesh with symmetry conditions to reduce computational cost (Fig. 8). Concrete, insulation, and formwork were explicitly modeled to capture thermal gradients and boundary effects.
Key inputs include:
- Convection coefficient of 10 W/m²K
- Hydration kinetics calibrated via calorimetry
- Experimentally measured autogenous shrinkage
Results and Validation
Temperature Validation
The numerical model reproduces temperature development with strong agreement:
- At embedded sensor locations
- Along insulated boundaries
This validation is critical, since temperature governs strain development.
Strain Predictions
Initial comparisons show:
- Numerical peak strains lower than measured values
- Post-peak behavior closely aligned
When interpreted against experimentally derived bounds, the agreement improves and falls in a realistic range, particularly during the cooling phase.
Interpretation: Governing Mechanisms of Early-Age Strain
Three potential sources of discrepancy were evaluated.
- Elastic Modulus Development: Limited influence due to low restraint conditions. Deformations are primarily driven by thermal expansion.
- Creep Modeling: Parametric variations confirm negligible impact on strain predictions for this case.
- Thermal Expansion Coefficient: This is the governing parameter. Experimental evidence (see Figure 11) shows that the thermal expansion coefficient is not constant, yielding higher values during early hydration, and showing reduction as the material transitions to a solid state.
Incorporating this variation into the numerical model significantly improves agreement with experimental results (Figure 12).
The revised model reproduces both heating and cooling behavior within experimentally defined bounds.
Key Outcomes
- Vibrating wire strain gauges are suitable for early-age monitoring when pre-solidarization effects are properly interpreted.
- Metallic sensors provide more reliable measurements due to lower temperature sensitivity.
- Early-age strain must be interpreted as a bounded quantity.
- Maturity-dependent thermal expansion is critical for accurate simulation.
- DIANA effectively reproduces coupled thermo-mechanical behavior when the development of material properties at early age is properly defined.
Conclusion
Early-age concrete behavior is governed by the interaction between temperature development and continuous stiffness gain. Temperature rises before the material can fully respond mechanically, and measurement systems reflect this lag.
Accurate prediction requires alignment between monitoring strategy, material modeling, and numerical formulation. DIANA provides a robust framework for integrating these components, but predictive accuracy depends on how early-age properties are defined.
Treating the thermal expansion coefficient as constant introduces systematic error during the most critical phase. Representing its development enables the model to capture the governing mechanisms and transition from approximation to reliable prediction.